Diane Hendricks and her late husband saw opportunity in Beloit, a decaying industrial town. Now, she dreams of turning it into a mecca for start-ups. When Diane Hendricks sees something she doesn’t like here, she buys it. A bankrupt country club. A half-empty mall. Abandoned buildings. The rusting foundry down by the river. Beloit used to be a town that made papermaking machines and diesel engines. Ms. Hendricks thinks it can be a place where start-ups create the next billion-dollar idea, and she is remaking the town to fit her vision. She can do so because she is the second-richest...